This application claims priority under 35 U.S.C. xc2xa7xc2xa7119 and/or 365 to 9704465-5 filed in Sweden on Dec. 1, 1997; the entire content of which is hereby incorporated by reference.
This invention relates in general to the field of electronic systems and more particular to an improved simulation system for bipolar transistors.
The cost and length of time required to produce an integrated circuit prohibits cut-and-try methods of varying component values and testing the resulting circuit until the desired performance is achieved. A more common way to test and evaluate circuit designs is to simulate the circuit design in a computer utilising mathematical models that characterise the different components incorporated in the circuit. The basic mathematical model characterising the behaviour of a bipolar transistor is the Gummel-Poon model. This model is described in U.S. Pat. No. 3,683,417 by Gummel where the fundaments of the Gummel-Poon model is outlined. The model assumes a constant Early voltage, independent of bias conditions and substrate potential.
In the Standard Gummel-Poon model, the Early effect and the high current injection is included in the current source ICT between the emitter and collector by introducing a variable for the base charge QB,                                           I            CT                    =                                                    I                SS                            ·                                                Q                  B0                                                  Q                  B                                                      ⁢                          (                                                exp                  ⁡                                      (                                                                  V                                                                              B                            xe2x80x2                                                    ⁢                                                      E                            xe2x80x2                                                                                              /                                              V                        T                                                              )                                                  -                                  exp                  ⁡                                      (                                                                  V                                                                              B                            xe2x80x2                                                    ⁢                                                      C                            xe2x80x2                                                                                              /                                              V                        T                                                              )                                                              )                                      ,                            (        1        )            
where VBxe2x80x2Cxe2x80x2 and VBxe2x80x2Exe2x80x2 are the internal junction voltages, ISS is the conventional intercept current with the y-axis in a Gummel plot, commonly called the saturation current, and VT is the thermal voltage.
The normalised majority base charge qb is defined as,
qb=QB/QB0,xe2x80x83xe2x80x83(1a) 
where QB is the actual base charge and QB0 is the zero-bias majority base charge.
The base charge qb is usually described with two variables:                                           q            b                    =                                                    q                1                            2                        +                                                                                q                    1                    2                                    4                                +                                  q                  2                                                                    ,                            (2a)            
where a first part of the base charge q1 is the variable that is modified, according to the invention, to enhance the Early voltage behaviour. A second part of the base charge q2 describes high injection of charges into the base, which can be neglected at low and intermediate current levels. An approximation of the base charge qb can therefore be used at low and intermediate current levels and for that purpose equation (2b) is approximated to,
qb≈q1.xe2x80x83xe2x80x83(2b) 
In the standard Gummel-Poon model, the Early voltages are assumed to be constant, independent of any variable, and modelled by the two parameters VAF0 and VAR, the forward and reverse Early voltages,                               1                      q            b                          =                  1          -                                    (                                                                    V                                                                  B                        xe2x80x2                                            ⁢                                              C                        xe2x80x2                                                                                                  V                    AFO                                                  +                                                      V                                                                  B                        xe2x80x2                                            ⁢                                              E                        xe2x80x2                                                                                                  V                    AR                                                              )                        .                                              (3a)            
In some simulations a slightly different expression may be used instead of equation 3a, e.g.                               q          b                =                  1          +                                    (                                                                    V                                                                  B                        xe2x80x2                                            ⁢                                              C                        xe2x80x2                                                                                                  V                    AFO                                                  +                                                      V                                                                  B                        xe2x80x2                                            ⁢                                              E                        xe2x80x2                                                                                                  V                    AR                                                              )                        .                                              (3b)            
A good approximation for high collector/emitter voltages, but a bit rough for low collector/emitter voltages is,
VCE≈VBxe2x80x2Cxe2x80x2,xe2x80x83xe2x80x83(4) 
xe2x80x83VBxe2x80x2Exe2x80x2≈0,xe2x80x83xe2x80x83(5)
and if the equations (2b), (4) and (5) are inserted into equation (3a), the following expression is obtained,                               1                      q            1                          =                              1            +                                          V                CE                                            V                AFO                                              =                                                                      V                  AFO                                +                                  V                  CE                                                            V                AFO                                      .                                              (        6        )            
Equation 6 will be used below when there is an Early voltage that is independent of the collector/emitter voltage VCE.
Other models have been developed to remove the deficiencies of the standard Gummel-Poon model (SGP), which have been apparent as process technology has advanced over time.
In IEEE Journal of Solid-State Circuits, Vol 31, page 1476, 1996, by McAndrew et al. an article with the title xe2x80x9cVBIC95, The Vertical Bipolar Inter-company Modelxe2x80x9d was presented, where improvements of the SGP was described. In an other article published in IEEE Transactions on Electronic Devices, Vol 32, page 2415, 1985, written by H. C. De Graaf and W. J. Kloosterman with the title xe2x80x9cNew Formulation of the Current and Charge Relations in Bipolar Transistor Modelling for CACD Purposesxe2x80x9d, another transistor model, called Mextram, was described. Amongst other improvements VBIC95 and Mextram includes a varying Early voltage model derived from physical relations.
The invention is not to be considered as a replacement to the above mentioned models, but as a useful complement to the SGP model, as well as other models. This is essential when the modelling of an accurate Early voltage is important or the cause of the Early voltage variation is not easily described by physical based relations.
When simulating the function of a bipolar transistor in a computer program, for example SPICE model simulation, a transistor normally is characterised by a slightly modified model of the above described Gummel-Poon model. There are several types of SPICE model simulation programs available on the market with one or several simulation models incorporated in the program, for example the Gummel-Poon model and an earlier Ebers-Moll model. The basic Ebers-Moll model does not simulate the behaviour of the Early voltage, but since it is simpler and involves less parameters it may be faster and more robust.
The SPICE model requires that the operator of the simulation give certain values of measured parameters of the bipolar transistors. The problem with the Gummel-Poon model is that it usually does not describe the behaviour of the Early voltage in a complete way, see FIGS. 1a and 1b. 
The present invention relates to a problem in simulating bipolar transistors where the Early voltage varies with collector/emitter bias voltages, VCE.
Another problem is in simulating bipolar transistors where the Early voltage varies with the substrate potential.
The object with the invention is to improve the standard Gummel-Poon model with an Early voltage extension, where the constant Early voltage is replaced by an Early voltage that is divided into several regions where the Early voltage is adjusted to fit the actual variation of a measured Early voltage characteristics of a bipolar transistor.
In accordance with the invention this object is achieved by means of apparatus incorporating a machine-implemented process that computes the Early voltage characteristics of a bipolar transistor from a set of parameters that may be obtained from direct measurements of the transistor itself.
One way of implementing this is to adjust the value of the Early voltage versus the collector/emitter bias voltages VCE in the following way. At low VCE, the constant Early voltage of the SGP model is replaced by a linear dependence on VCE. At intermediate values on VCE a constant Early voltage corresponding to the single Early voltage in the SGP model is used. At high VCE, the constant Early voltage of the SGP model is replaced with an increased constant value of the Early voltage where the break point between the constant Early voltages is dependent on the substrate potential. The base charge is recalculated from a differential equation, which is solved in each region, and linked together through the choice of boundary conditions. The solution of the differential equation is then included in the mathematical model describing the Early voltage dependency. This improved model is called QTEC.
An advantage of the present invention is an improved collector output characteristics.
Another advantage is that, apart from a few modifications, old parameters from a previous device characterisation against the standard Gummel-Poon model can be maintained.
Yet an advantage is that simple expressions can be used, which will not severely degrade the simulation time or convergence properties.
Yet another advantage is that the invention provides a continues collector current, and the possibility to model continues derivatives as well.
Yet another advantage is that the invention will provide an enhanced simulation model of bipolar transistors, particularly for high voltage bipolar transistors, at all bias conditions.